Metamaterials are artificially structured materials in which both the electric permittivity and the magnetic permeability μ are tunable. Such materials can possess a negative index of refraction and are sometimes referred to as “left-handed,” when the wave vector is antiparallel to the usual right-handed cross product of the electric and magnetic fields characteristic of naturally occurring materials. Metamaterials have electromagnetic properties that are difficult or impossible to achieve with conventional right-handed materials, the most notable being the negative refractivity. These unconventional properties suggest a number of unique applications, including compact aberration-free lenses, subwavelength imaging, and cloaking. However, although materials with negative electric permittivity are readily available at low frequencies, including metals below the ultraviolet region and doped semiconductors in the terahertz and infrared regions, existing materials with negative magnetic permeability typically lose their magnetic activity at much lower frequencies. Therefore, until recently, artificial metamaterials having both negative permittivity and negative permeability in the same frequency range were difficult to realize in practice.
However, in the late 90s, Pendry proposed a practical split-ring resonator (SRR) structure that can be used to achieve a negative permeability in the vicinity of a magnetic resonance frequency. See J. B. Pendry et al. IEEE Trans. Microwave Theory Tech. 47, 2075 (1999). When combined with continuous wires, one can simultaneously obtain a negative permittivity and a negative permeability, thereby exhibiting a left-handed index of refraction. See D. R. Smith et al., Phys. Rev. Lett. 84, 4184 (2000). As shown in FIG. 1 the simplest form of the SRR 10 is planar metallic ring 11 with a gap 12. The ring 11 has an outer dimension l and a metal linewidth w. The gap 12 has a width g. In essence, the SRR 10 is a small LC circuit consisting of an inductance L and a capacitance C. The ring 11 forms one winding of a coil (the inductance), and the ends form the plates of a capacitor. Electromagnetic radiation directed into the plane of the SRR induces a ring current I in the ring. Metamaterials comprise an array of such subwavelength metallic resonator structures within or on an electrically insulating or semiconducting substrate. Dense packing of SRRs, using lattice constants smaller than the LC resonance wavelength, creates a metamaterial that can exhibit a magnetic and electric resonance at the resonant frequency, ωLC=1/√{square root over (LC)}. Two resonances are observed when exciting the SRR structure shown with incident radiation having polarization perpendicular to the gap (i.e., electric field E parallel to the arm containing the gap, as shown). The LC resonance corresponding to the ring current leads to a magnetic dipole moment perpendicular to the SRR plane and an electric dipole moment parallel to the incident electric field. A shorter wavelength Mie resonance is also excited, corresponding to an electric dipole oscillating in the arm opposite the gap. With incident radiation polarized parallel to the gap, only a Mie resonance corresponding to electric dipoles oscillating in the two arms parallel to the gap is observed. The resonances can be strengthened by adding additional, concentric rings, each ring having a gap, to the simple SRR structure. Other resonant structures can also be designed and implemented.
In principle, the resonator response is scalable from radio to infrared and optical frequencies. See D. R. Smith et al., Phys. Rev. Lett. 84, 4184 (2000); J. B. Pendry et al., Science 312, 1780 (2006); R A. Shelby et al., Science 292, 77 (2001); and C. Enkrich et al., Phys. Rev. Lett. 95, 203901 (2005). For the simple SRR described above, both the inductance and capacitance scale proportionally to SRR size, provided that all SRR dimensions are scaled down simultaneously and that the metal retains a high conductivity. Therefore, the resonant frequency scales inversely with a normalized size. Therefore, metamaterials have the potential to provide a scale-invariant design paradigm to create functional materials which can enhance our ability to manipulate, control, and detect electromagnetic radiation.
In practice, however, extrapolation of metamaterial concepts to shorter wavelengths has challenged every aspect of design, electromagnetic modeling, micro-fabrication and optical characterization. Material losses have scaled non-linearly with reduction in dimension, while the design space has focused predominately on planar SRRs, cut-wire pairs (CWPs), or fishnet-like structures. In particular, ohmic losses in metal become significant at optical/IR frequencies. Fabrication of planar optical/IR metamaterial structures such as SRRs and CWPs typically requires advanced lithography, such as e-beam, just to achieve patterning at these dimensions. For example, infrared metamaterials require linewidths in the hundreds of nanometers size scale, which is difficult for all but cutting edge lithography. See J. B. Pendry et al., IEEE Trans. Microwave Theory and Tech. 47, 2075 (1999); V. M. Shalaev et al., Optics Lett. 30, 3356 (2005); and S. Zhang et al., Phys. Rev. Lett. 95, 137404 (2005).
Further, planar metamaterial structures are highly anisotropic. Therefore, many device applications require the fabrication of three-dimensional (3D) metamaterials. Such 3D structures enable full coupling of incident electromagnetic radiation in two or three orthogonal directions. 3D metamaterial fabrication at microwave frequencies is aided by the ability to fabricate optimal resonator structures and then assemble them into the optimal 3D metamaterial geometry. However, the creation and assembly of 3D geometries at size scales required for IR and optical metamaterials is inherently difficult. In particular, the placement/orientation of the resultant structure out of the plane of fabrication is not currently possible at scales suitable for IR and optical frequencies. The vision of truly isotropic 3D metamaterials operating in the IR and visible wavelength ranges will require breakthrough advances in fabrication to achieve relevant sub-wavelength dimensions. As a result, most published work on fabrication of 3D metamaterials in the optical/IR wavelength range leverages e-beam written planar or stacked planar structures, while modeling has predominately focused on planar, stacked planar, and/or 3D cubic structures.
The present invention enables the fabrication of 3D metamaterials with micron-scale characteristic dimensions. The method relies on standard lithography to create the canonical metamaterial resonator geometry (SRR, CWP, etc), but then uses a combination of processing sequence and directional projection evaporation to replicate the resonator geometry onto surfaces normal to the lithography plane. The invention also enables fabrication of resonators on curved surfaces with radius of curvature on the order of the size of the resonator. The result is a methodology for construction of complex 3D metamaterial structures. The process is scalable to large areas and can be stacked to achieve macroscopic 3D volumes of material.